+267 Let A(t) = 3- 2t^2 + 4^t. Find A(2) - A(1).
The function f satisfies f(sqrt(x+1)) = 1/x for all $x >= -1, x does not equal 0. Find f(2).
Thanks :D
+9479 A(t) = 3 - 2t2 + 4t
A(2) = 3 - 2(2)2 + 42
A(1) = 3 - 2(1)2 + 41
A(2) - A(1) = [ 3 - 2(2)2 + 42 ] - [ 3 - 2(1)2 + 41 ]
A(2) - A(1) = [ 3 - 2(4) + 16 ] - [ 3 - 2(1) + 4 ]
A(2) - A(1) = [ 3 - 8 + 16 ] - [ 3 - 2 + 4 ]
A(2) - A(1) = [ 11 ] - [ 5 ]
A(2) - A(1) = 6
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f( √[x + 1] ) = 1/x for x ≥ -1 and x ≠ 0
We want to find f(2) , so we need an x value that makes
√[ x + 1] = 2 square both sides
x + 1 = 4 subtract 1 from both sides
x = 3 This is a valid x to plug in.
So....
f( √[3 + 1] ) = 1/3
f( 2 ) = 1/3 
+9479 A(t) = 3 - 2t2 + 4t
A(2) = 3 - 2(2)2 + 42
A(1) = 3 - 2(1)2 + 41
A(2) - A(1) = [ 3 - 2(2)2 + 42 ] - [ 3 - 2(1)2 + 41 ]
A(2) - A(1) = [ 3 - 2(4) + 16 ] - [ 3 - 2(1) + 4 ]
A(2) - A(1) = [ 3 - 8 + 16 ] - [ 3 - 2 + 4 ]
A(2) - A(1) = [ 11 ] - [ 5 ]
A(2) - A(1) = 6
----------
f( √[x + 1] ) = 1/x for x ≥ -1 and x ≠ 0
We want to find f(2) , so we need an x value that makes
√[ x + 1] = 2 square both sides
x + 1 = 4 subtract 1 from both sides
x = 3 This is a valid x to plug in.
So....
f( √[3 + 1] ) = 1/3
f( 2 ) = 1/3
